Fig. 155.
Take, for example, the following train of five wheels, even numbers being given for the sake of clearness, to represent the circumferences or number of cogs in each, [Fig. 156]. We have here, as the first and last, 6 in. and 120 in., and, if in contact, the first must revolve 20 times, while the latter revolves once. Interpose the three idle wheels of 10, 30, and 60 in. respectively. During one revolution of the largest wheel, the second will revolve twice, the third four times, the fourth twelve times, the fifth twenty times, the same precisely as if the first and last had been in immediate contact. The range of a slide rest-screw is quite long enough for many purposes of the amateur, and a connection thus made between the mandrel and such screw is what may be termed a miniature of the arrangement adopted in the large self-acting lathes. In the latter, however, a leading screw is added the full length of the bed along which the slide rest travels bodily. We may, therefore, consider the screw of the slide-rest a leading screw, and make use of the rules applied in the case of large lathes to decide the proportions of wheels required to cut a given screw. It is plain that when the pitch of the required screw is greater than that of the leading screw, the revolution of the latter must be at a quicker rate than the former. If, for instance, a spiral is to be cut, like the Elizabethan twist, containing but one perfect thread in two inches, while the leading screw contains twenty threads in the inch, or forty in the 2 in., the latter must be arranged to make forty revolutions while the former makes one, because it takes 40 revolutions to carry the tool along 2 in., which is the pitch of the required spiral. The two outside wheels must therefore bear that proportion to one another. Forty to one, however, would be a practically difficult ratio, to place as described, even a pinion of ten teeth on the leading screw requiring 400 teeth on the chuck. Hence a different arrangement would be necessary if such very great difference exist between the pitch of the leading or rest screw and that to be cut. The same obvious difficulty would occur where a very fine screw is required, and the pitch of the leading screw is coarse. This will have to be referred to again. One example, therefore, of the method of overcoming this difficulty will suffice. A train of wheels is shown in [Fig. 157], of which A has 60 teeth, B 10 teeth, C, on the same axle and united to C, 30 teeth, D 20 teeth. While A turns once, B will turn six times, C necessarily six times also, D nine times. In this case, if the first and last had geared together D would have made but three turns, while A made one.
Fig. 156.
Fig. 157.
The following is an easy method of calculating a series of such change wheels:—
Write down the number of threads in the screw to be cut, and also the number of threads in the leading screw; multiply both by any convenient number likely to give such results as to tally with the cogs in the set of change wheels. Suppose it is desired to cut eight threads to the inch, and that the leading screw has two threads in that length. Then: